I find it interesting that the ocean currents are represented as 2D grids rather than 3D structures. I presume there is some physics at work which makes a 2D simulation sufficient. Still, I wonder what it would do to our grid solver if we had a 3D grid?
If we blocked by cubes instead of squares, each point would need to communicate with 6 other points rather than 4, which increases the arithmetic cost of the task. However, communication costs should be lower, I think, if we consider the surface area to volume ratio of a cube vs the perimeter to area ratio of a square. Not entirely sure what the affect would be on cache locality, would depend on how the 3D grid was represented in memory.
I can't really make a proper analysis between a 2D and 3D problem's performance, since the tasks require different work, but I found myself wondering how the techniques could be scaled up with dimension rather than size.
I find it interesting that the ocean currents are represented as 2D grids rather than 3D structures. I presume there is some physics at work which makes a 2D simulation sufficient. Still, I wonder what it would do to our grid solver if we had a 3D grid?
If we blocked by cubes instead of squares, each point would need to communicate with 6 other points rather than 4, which increases the arithmetic cost of the task. However, communication costs should be lower, I think, if we consider the surface area to volume ratio of a cube vs the perimeter to area ratio of a square. Not entirely sure what the affect would be on cache locality, would depend on how the 3D grid was represented in memory.
I can't really make a proper analysis between a 2D and 3D problem's performance, since the tasks require different work, but I found myself wondering how the techniques could be scaled up with dimension rather than size.